Question

What is the graph of the solution to the following compound inequality? –6x – 1 < –25 or 3x + 4 ≤ –5

Answer 1

`x>4` or
`x \leq -3`

Explanation:

Given :
`-6x -1 < -25` or
`3x + 4 \leq -5`

Solving first inequality :

`-6x-1<-25`

Add 1 to both sides

`\Rightarrow -6x-1+1<-25+1\\\Rightarrow -6x<-24\\\Rightarrow 6x>24`

Divide both sides by 6

`\Rightarrow (6)/(6)x>(24)/(6)\\\Rightarrow x>4`

Solving second inequality:

`3x + 4 \leq -5`

Subtract 4 from both sides

`\Rightarrow 3x+4-4 \leq -5-4\\\Rightarrow 3x \leq -9`

Divide both sides by 3

`\Rightarrow (3)/(3)x \leq (-9)/(3)`

`\Rightarrow x \leq -3`

So,
`x>4` or
`x \leq -3`

Refer the attached graph